iZenBridge's PMP® Math Series: Project Selection : PV , NPV, IRR, BCR and Payback Period

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PMP®

Math Series

Economic Model


Present Value

Net Present Value

Internal Rate of Return

Benefit Cost Ratio

Payback Period


The time value of money.

The money you get in 5 years isn’t worth as money

you get today


Present Value


Present Value

• Value today of the future cash flow

• Present Value = FV / (1 + i)^ n

• i = Discount rate

• n = Period

• FV = Future Cash Inflow/ Outflow

Now

Year 1

Year 2

Year 3


Present Value

• Discount Rate = 10%

• PV = 4000 / (1+10/100) ^2

• PV = 4000/ (1.1) ^2

• PV = 4000 / 1.21

• PV = 3305

• It mean 3305 USD earned today is equals to 4000 USD earned

after two year

Now

Year 1

Year 2 4000 USD


Which Investment Option is Better ?

Option A :

Returns: 4000 USD after 2

years

Option B:

Returns: 3500 USD after 1

years

Discount Rate =

10% per annum

PV = 4000/(1.1) ^2

= 3305 USD PV = 3500/(1.1)

= 3181 USD


Usages of Present Value (PV)

• Used as a base for calculating the Net Present Value (NPV)

• Simple investment decisions can be made using this technique

• Higher the PV the better the investment


Net Present Value (NPV)


Net Present Value (NPV)

• NPV is a measure of how much money a project can be

expected to return (in today’s present value).

• It’s a Sum of Inflow and outflow in present value term (mean

discounted based on duration)

Now

FV 1 (Year 1)

FV 2 (Year 2)


Net Present Value

NPV = Sum (PV)

= Sum (FV / (1 + i)^ n)

i = Discount rate

n = Period

FV = Future Cash Inflow (+) / Outflow (-)


Net Present Value

• Discount Rate = 10%

• NPV = -1000-1000 /((1+10/100) ^1)

• + 4000/((1+10/100)^2)

• = -1000 – 909 +3306

• = 1397 (This Project returns 1397 USD in present value

term)

Outflow 1000 USD (Now)

Outflow 1000 USD (Year 1)

Inflow 4000 USD (Year 2)


Which Project to Select?

• Project A has a duration of 4 years and an NPV of $40,000,

• Project B has a duration of 3 years and an NPV of $45,000,

• Project C has a duration of 6 years and an NPV of $62,000

Which project will you select?

Go with Project C, Time value of money already considered in

NPV so years doesn’t matter


Usages of Net Present Value (NPV)

• One of the frequently used tools for project selection

• Take in account inflow and outflow of cash

• Easy to calculate

• A negative value indicates that we are loosing money

• Higher the NPV the better the project


Internal Rate of Return (IRR)



• IRR is a measure of how quickly the money invested in a

project will increase in value. It’s a rate of return which

calculate based on the inflow and outflow of the project.



• The rule is same like NPV, the difference is, now we need to

compute the rate (i) which equalizes the cash inflow and

outflow

0 = Sum (FV / (1 + i) ^ n)

i = IRR this is what we calculate

n = period


Internal Rate Return (IRR)

• 0 = -1000-1000 /((1+i/100) ^1) + 4000/((1+i/100) ^2)

• If we put i = 56, it makes the equation balance, so in this case

IRR = 56%

Outflow 1000 USD (Now)

Outflow 1000 USD (Year 1)

Inflow 4000 USD (Year 2)



• Which Project you will select?

Project Name IRR Investment

Gold 6% 4,500,000

Silver 5.8% 1,700,000

Platinum 5.4 % 2,000,000

Copper 3% 1,000,000


Usages of Internal Rate of Return (IRR)

• Frequently used in Project selection

• It does not require assumption of discount rate

• Gives the result in % term rather than absolute

• Higher the IRR the better the project


NPV represents the

project benefit in

absolute term like

100,000 USD

IRR represents the value

in proportion like 10%,

56%

We can get contradictory recommendations

from NPV and IRR, but in exam you do not

get such questions

NPV vs IRR


Benefit Cost Ratio


Benefit Cost Ratio

• Money project going to make versus its cost.

• Benefit/Cost OR Revenue/cost

• Remember : Revenue is not equals to Profit


Benefit Cost Ratio (BCR)

• Greater Benefit<->Greater Ratio <-> Better project


Benefit Cost Ratio (BCR)

• Which of the following projects do you select?

• A) Project Gold with a BCR of 0.9

• B) Project Silver with a CBR of 0.9 and cost of $100,000

• C) Project Diamond with a cost of $100,000 and benefits of

$110,000

• D) Project Platinum with a BCR of 1.2

a) 0.9 b) BCR = 1/0.9 = 1.11 c) 11/10 = 1.1 d) 1.2

• Answer: D


Usages of Benefit Cost Ratio

• Ratio helps in visualizing the relative value

• May calculate considering Time Value of Money

• Simple to calculate and explain

• Ratio less than 1 indicate we are losing money

• Higher the value, the better it is.


Payback Period


Payback Period

• Time required to get originally invested amount back

• Smaller is better . Earlier we get money, better it is


Payback Period

• Project A requires investment of $500,000. The project is

expected to generate $25K per quarter for the first year and

$100K per quarter after that. What is the payback period?

By when I get 500,000 Back?

First Year = 25K + 25K + 25K + 25K = 100K

(still need 400K)

Second Year = 100K + 100K+100K+ 100K =

400K (Done)


Usages of Payback Period

• Helps in looking the investment in time dimension

• The sooner we get our money back is better

• Usually calculated without considering the time value of money

• One can calculate discounted payback period


Exam Tip

Present Value

Higher is Better

Net Present Value

Higher is Better

Internal Rate of Return

Higher is Better

Benefit Cost Ratio

Higher is Better

Payback Period

Shorter is Better


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iZenBridge's PMP® Math Series: Project Selection : PV , NPV, IRR, BCR and Payback Period

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Transcript of iZenBridge's PMP® Math Series: Project Selection : PV , NPV, IRR, BCR and Payback Period